欧洲央行-如何在VAR模型中进行贝叶斯联合推理？（英）

Working Paper Series How to conduct joint Bayesian inference in VAR models? Andrian Yambolov Disclaimer: This paper should not be reported as representing the views of the European Central Bank (ECB). The views expressed are those of the authors and do not necessarily reflect those of the ECB. No 3100 AbstractWhen economic analysis requires simultaneous inference across multiple variablesand time horizons, this paper shows that conventional pointwise quantiles in Bayesianstructural vector autoregressions significantly understate the uncertainty of impulseresponses. The performance of recently proposed joint inference methods, whichproduce noticeably different error band estimates, is evaluated, and calibrationroutines are suggested to ensure that they achieve the intended nominal probabilitycoverage. Two practical applications illustrate the implications of these findings: (i)within a structural vector autoregression, the fiscal multiplier exhibits error bandsthat are 51% to 91% wider than previous estimates, and (ii) a pseudo-out-of-sampleprojection exercise for inflation and gross domestic product shows that joint inferencemethods could effectively summarize uncertainty for forecasts as well.Theseresults underscore the importance of using joint inference methods for more robusteconometric analysis.Keywords: vector autoregressions, impulse responses, forecasts, pointwise inference, joint inferenceJEL Codes: C22, C32, C52ECB Working Paper Series No 31001Non-technical summaryStandard methods for constructing error bands around impulse response functions considerthem in isolation, neglecting the estimation uncertainty that arises across variables and timehorizons due to the joint nature of the underlying structural parameters. For example, oneapproach to assessing the impact of government expenditure on economic activity—known asthe fiscal multiplier—is to estimate the ratio between the cumulative responses of gross domesticproduct and government expenditure. By convention, practitioners use marginal error bands toaddress this and similar economic questions, which leads to an underestimation of uncertainty.This paper quantifies the extent to which conventional error bands understate uncertainty andfocuses on methods for conducting joint inference to support more robust economic analysis.It conducts a series of simulation experiments using widely adopted Bayesian vector autore-gressions to evaluate the performance of several estimators, discussed by Montiel Olea andPlagborg-Møller (2019) and Inoue and Kilian (2022), that account for the joint uncertainty ofimpulse response functions. In addition, it proposes strategies to improve upon those jointinference methods, which tend to overstate the uncertainty.The policy relevance of the paper is illustrated through two examples. The first draws on awidely used fiscal vector autoregression estimated with U.S. data. It shows that taking intoaccount the joint uncertainty between gross domestic product and government